Submission date: 13 September 2020

Abstract:

We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collapse of the groupoid in an earlier work of the second author), and relating it to orthogonality, triviality of fibrations, the strong canonical base property, differential Galois theory, and GAGA.

We prove that DCF_0 does not have the strong canonical base property, correcting an earlier proof. We also prove that the theory CCM of compact complex manifolds does not have the strong CBP, and initiate a study of the definable Galois theory of projective bundles. In the rest of the paper we study definable fibrations in DCF_0, where the general fibre is internal to the constants, including differential tangent bundles, and geometric linearizations. We obtain new examples of higher rank types orthogonal to the constants.

Mathematics Subject Classification: 03C45, 12H05

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Full text arXiv 2009.06014: pdf, ps.